Using your Head is Permitted

June 2008 riddle

Arthur is planning a multi-evening dinner-party to be set in Camelot. His plan is to invite n couples, making a total of 2n+1 guests (including Arthur himself), and to seat these guests around his famed "round table".

Each person at the party therefore has one person to his right and one to his left on each night of the party, and Arthur's plan is to keep the conversation lively by re-shuffling the order in which the guests are to sit each night so that no two people will spend more than one night in adjacent chairs.

Clearly, this can not go on for more than n nights, after which each guest at the party will have sat next to all 2n other invitees.

Arthur's question is this: for which values of n is it possible for the party to last the whole n nights planned (before two people sit adjacent to each other on multiple occasions)?

Hint: Readers are encouraged to investigate the "unidirectional" version of this riddle, in which no person is allowed to sit to the right of the same person twice, even though she may sit once to his right and once to his left.

List of solvers:

Bojan Bašić (4 June 18:50)
Hongcheng Zhu (6 June 12:23)

Elegant solutions can be submitted to the puzzlemaster at Names of solvers will be posted on this page. Notify if you don't want your name to be mentioned.

The solution will be published at the end of the month.


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